Ground states for scalar field equations with anisotropic nonlocal nonlinearities. (English) Zbl 1335.35034
Summary: We consider a class of scalar field equations with anisotropic nonlocal nonlinearities. We obtain a suitable extension of the well-known compactness lemma of V. Benci and G. Cerami [Arch. Ration. Mech. Anal. 99, 283–300 (1987; Zbl 0635.35036)] to this variable exponent setting, and use it to prove that the Palais-Smale condition holds at all level below a certain threshold. We deduce the existence of a ground state when the variable exponent slowly approaches the limit at infinity from below.
MSC:
| 35J20 | Variational methods for second-order elliptic equations |
| 46B50 | Compactness in Banach (or normed) spaces |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
Keywords:
scalar field equation; anisotropic nonlocal nonlinearity; variable exponent; loss of compactness; existence of ground stateCitations:
Zbl 0635.35036References:
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